Digitally implemented fast frequency estimator/demodulator for low bit rate maritime and mobile data communications without the use of an acquisition preamble

ABSTRACT

A low-bit-rate, low-cost, all-digital preambleless demodulator for maritime and mobile data communications operates under severe high noise conditions, fast Doppler frequency shifts, large frequency offsets, and multipath fading. Sophisticated algorithms, including an FFT-based burst acquisition system, a cycle-slip resistant carrier phase tracker, an innovative Doppler tracker, and a fast acquisition symbol synchronizer, provide reliable burst reception. The compact DSP-based demodulator includes an input buffer receiving a complex sampled baseband input signal and providing a baseband output to a coarse frequency estimator fast Fourier transform (FFT) or discrete Fourier transform (DFT) module which produces a first estimation of the carrier frequency. A fine frequency estimator FFT or DFT module receives the first estimation and provides a second estimation of the carrier frequency. An extra coarse frequency estimator FFT or DFT module may be provided between the buffer and the coarse frequency estimator.

This is a continuation-in-part of application Ser. No. 07/800,020, filedNov. 29, 1991 and now abandoned.

BACKGROUND OF THE INVENTION

The present invention relates to a digitally implemented demodulator formaritime and mobile data communications, and in particular to a fastfrequency estimator which operates without using an acquisitionpreamble.

A typical packet format used for burst communications and signaling in atime division multiple access (TDMA) network employs a structure thatincludes an acquisition preamble at the start of the packet, followed bya known unique word (UW) pattern. The data portion of the packet thenfollows, with additional framing bits inserted periodically for longpackets, with the packet ending in another known "end-of-packet"sequence.

The acquisition preamble that precedes the data portion of the packettypically incorporates an unmodulated carrier sequence for the carrierfrequency and phase estimate at the receiver, followed by a clockrecovery sequence for proper receiver clock phase alignment. The UWpattern is used for phase ambiguity resolution and burst timesynchronization. After the preamble and UW segments have been receivedand acted upon, the receiver is ready to demodulate the ensuing datasegment with the correct frequency, phase, and clock adjustments.

The unmodulated carrier segment appears as a single tone in thefrequency spectrum for a short duration. The detection of the carriercan therefore be accomplished by frequency domain acquisitionalgorithms.

In an analog implementation, a frequency lock loop (FLL) may be used. Abank of analog bandpass filters followed by energy detectors may be usedto give a coarse estimate of carrier frequency. A similar techniqueutilizes a bank of correlators tuned to several discrete carrierfrequencies. In a digitally implemented receiver, a DFT/FFT-basedalgorithm may be used. Time domain techniques may also be used for thecarrier frequency estimate, whereby the unmodulated carrier phasedifferences are computed periodically and an average estimate isobtained that is indicative of the rate of the phase change or thefrequency offset.

The methods used for carrier frequency acquisition described above havelimitations that preclude their use for communication networks thatoperate under hostile channel environments that include lowsignal-to-noise levels, large frequency offsets, Doppler frequencyshifts, and multipath fading. The FLL technique, in particular, requiresa finite "lock-in" time for the loop to acquire. The tracking range isalso very limited if a high-resolution measurement is required. For datapackets with very short acquisition preambles, or for preamblelesspackets, the FLL technique is disadvantageous. The FLL method may stillbe used during the data portion of the packet if the signal is squaredto remove the modulation (for binary phase shift keying, or BPSK) butwith a corresponding loss of operating signal-to-noise ratio that willcompromise its operation for low channel signal-to-noise ratios.

The bandpass filter and correlator approaches become excessively complexif a very high resolution measurement is required. If the filters orcorrelators are of the analog type, they are also subject to drift andrequire precise components and frequent adjustments. In addition, signaldetection is sensitive to the input signal level unless an automaticgain control (AGC) circuit is employed.

The straightforward FFT technique suffers the disadvantage ofsusceptibility to multipath that will affect the signal strengths in thefrequency bins. A single DFT or FFT must also be very large (1024 pointsor greater) to operate successfully at very low values of E_(S) / N_(O).A threshold to detect the signal presence will be unreliable unlessexternal AGC is employed that will track the multipath fading. Atradeoff DFT/FFT computation time versus frequency resolution is alsonecessary. Fine frequency resolution translates to longer FFTcomputation time, and vice versa. In addition, this technique is suitedfor the case of a packet with an acquisition preamble. For preamblelesspackets, the straightforward FFT technique requires modifications.

The time domain frequency estimation technique is dependent on theunmodulated portion of the acquisition preamble, and is totally unsuitedfor preambleless packets. This method is also particularly sensitive tothe magnitude of the frequency offset. If the frequency offset is largeenough to cause a rotation of the signal vector through 2π radiansbetween the periodic estimates, then the measurement will be in error.In addition, due to the low operating signal-to-noise ratios, a longtime average of the phase difference measurements are required, thusnecessitating a long acquisition preamble.

The required preamble that precedes the data portion of the packet oftenconstitutes an excessive overhead that reduces the channel transmissionefficiencies for short data packets. Particularly in the case of mobileand maritime communication networks that experience signal fades ofvarying degrees, the system design mandates the use of very short databursts (approximately a few hundred bits) that are relatively immune tofades. These bursts generally are used for the channel request andassignment functions from the remote terminal to a central location,typically a network coordination center. With additional channelimpairments such as Doppler shifts, low carrier-to-noise ratios, andfrequency offsets, long acquisition preambles usually are required tolocate the carrier correctly, and to acquire its frequency and phase.The use of a long preamble in this case is an extremely undesirableoverhead that seriously undermines the channel transmission efficienciesfor a large communication network, with potentially thousands of suchremote terminals.

SUMMARY OF THE INVENTION

In view of the foregoing, it is an object of the present invention toprovide a compact, low bit rate, low cost, all-digital burst demodulatorthat requires absolutely no acquisition preamble. Both the acquisitionalgorithms and the hardware architecture are applicable under a widevariety of system constraints, and are particularly well suited forreception of short data packets under very adverse channel conditions.

In accordance with the present invention, a digitally implemented fastfrequency estimator has been devised for application in low bit ratemaritime and mobile MPSK-modulated (M'ary phase shift keying) datacommunication that performs reliably under severe channel conditions,such as low signal-to-noise ratios, large frequency offsets andmultipath fading. The estimator is well suited for carrier frequencyestimation for short burst packets, particularly for those packets thatdo not have an acquisition preamble preceding the data portion, such asthe preambleless packet used for the INMARSAT Standard-C signallingchannel. The estimator detects signal presence independent of the inputsignal level, eliminating the need for automatic gain control. Theestimation technique is particularly suited for implementation in adigital signal processor. The limitation on the operating bit rate istherefore solely a function of the processor speed.

In implementation, a two step process, using Discrete Fourier Transforms(DFT) or Fast Fourier Transforms (FFT), is used. The first step involvestaking a time average of a sequence of hopping FFTs, with the samplewindow slid sequentially by half the window length for each such DFT/FFTcomputation. A time average of the signal energy in each of the DFT/FFTfrequency "bins", followed by a relative energy level comparison betweenthe bins, yields (a) a detection of the burst presence, and (b) thelocation of the carrier and its offset frequency from the referencefrequency. The coarse carrier frequency is resolved to ±75 Hz in thefirst step. The second step involves performing another DFT/FFT aroundthe frequency range identified by the first step to yield a finefrequency estimate resolved to less than 10 Hz.

The present invention embodies several improvements and enhancementsover the old methods described above. A summary of the advantages is asfollows:

1. The estimator operates on MPSK modulated data directly, eliminatingthe requirement of a carrier acquisition preamble sequence;

2. The use of separate coarse and fine estimators allows carrieracquisition over a very wide frequency range (greater than the MPSKsymbol rate) at very high resolution (<1% of the symbol rate). Thisresolution accuracy, under conditions of large frequency offsets, lowsignal-to-noise ratios and multipath fading, is a major improvement inthe DFT/FFT-based method. In one embodiment of the invention, anadditional estimator stage is added, yielding a multi-stage approachwhich enables yet further improvement;

3. Time averaging of the measured signal strengths in each of theDFT/FFT frequency bins increases the signal-to-noise ratio of themeasurement, making its operation possible even at very low channelsignal-to-noise values;

4. The use of "time-hopped" DFT/FFTs with the sample window moved byhalf the window width for each DFT/FFT computation provides theadvantage of minimizing the variance of the estimation while drasticallyreducing the number of computations as compared to DFT/FFTs slid in timeby 1 sample period;

5. Relative energy level comparison between DFT/FFT bins removes theeffect of signal strength variations due to multipath fading and inputgain variations. Signal activity is detected independent of the inputsignal level. As a result, there is no need for an AGC as otherwisetypically would be employed. The result of performing operations (3),(4), and (5) yields not only the detection of the burst presence, butalso locates the carrier and determines its offset frequency from thereference frequency;

6. The use of sample rate decimation between stages greatly reduces thecomputational complexity compared to other FFT based approaches. Actualimplementation of this algorithm has been optimized for digital signalprocessor-based (DSP) demodulators. Thus, with the DSP assembly languagecode already developed, an increase in the operating bit rate is readilyachieved by migrating the code to faster processor versions in the sameDSP family or to another faster processor of a different family.

The use of the second DFT/FFT for the fine frequency estimation and theapplication of this technique for the coarse and fine frequencyestimations for preambleless data packets are particularly importantfeatures of the inventive method. The use of multiple DFT/FFT stages forcarrier frequency estimation, in which the output of each precedingstage is fed to the next stage, greatly increases the frequencyresolution at each stage.

U.S. Pat. No. 4,466,108, commonly assigned with the present application,discloses a technique for performing phase shift keying (PSK)synchronization without requiring a preamble. However, the techniquedisclosed therein does not use the multiple-stage DFT/FFT approach ofthe present invention, inter alia, as will be discussed herein.

Other known techniques, such as that disclosed in U.S. Pat. No.4,245,325, use an FFT technique, but for a very different purpose fromthat of the invention. U.S. Pat. No. 4,912,422 uses multiple FFT stages,but uses the resulting frequency estimate to steer a separate set ofbandpass filters, whereas in the present invention FFT and filteringprocesses are combined in a single operation.

Other patents considered to be possibly relevant background to thepresent invention include U.S. Pat. Nos. 4,528,567; 4,618,830;4,654,667; 4,689,806; 4,827,488; 4,870,420; and 4,885,756.

Two embodiments of the software algorithms to be implemented in thehardware embodiments of the invention are described herein. The secondembodiment has greater flexibility than the first in terms ofoperability at different symbol rates. In particular, the secondembodiment provides yet another, extra coarse resolution DFT/FFT stage,yielding a total of three DFT/FFT stages. The addition of the "extracoarse" stage estimates the frequency of the modulated spectrum. Theinput signal is not preprocessed by a squaring operation, as has beendone traditionally to remove the modulation first. As a result,performance at low S/N ratios is improved greatly, since squaring candegrade the S/N ratio by more than 6 dB. The first, "extra coarse" stageacts to filter the input signal to remove a significant amount of noise.Squaring then is employed in the second stage, where the impact of thedegradation is not as great.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and advantages of the invention will beunderstood from the following detailed description taken in conjunctionwith the accompanying drawings, in which:

FIG. 1 shows a preambleless packet format for the Inmarsat-C signalingchannel, at two different symbol rates;

FIG. 2 is a functional block diagram in accordance with a firstembodiment of the present invention;

FIG. 3 is a block diagram of the Doppler estimator and frequency trackerof FIG. 2;

FIG. 4 is a block diagram of a phase tracker and bit detector used inconnection with the Doppler estimator and frequency tracker of FIG. 3;

FIG. 5 is a structural hardware block diagram of a first embodiment ofthe present invention;

FIG. 6 is a block diagram of a test setup used to test the algorithmsused in the preambleless demodulator according to the present invention;

FIG. 7 is a functional block diagram of the inventive frequencyacquisition algorithm implemented in Inmarsat-C Coast Earth Station(CES) signalling/message demodulators in accordance with the firstembodiment;

FIG. 8 is a functional block diagram of a frequency acquisitionalgorithm in accordance with a second embodiment of the presentinvention;

FIG. 9 is a functional block diagram of a frequency acquisitionalgorithm in accordance with a modification of the second embodiment ofthe present invention;

FIG. 10 is an overall block diagram of a three-stage frequency estimatorin accordance with the second embodiment of the invention; and

FIG. 11 is a functional block diagram of a frequency acquisitionalgorithm in accordance with the embodiment of FIG. 10.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In order to illustrate the inventive frequency acquisition algorithmsand their hardware implementation, the preambleless short data packetformat from a new maritime communication network, designated as"Standard-C" or "Inmarsat-C", which has already been specified by theInternational Maritime Satellite Organization, (INMARSAT), will be used.The preambleless short data packet format is used for the slotted ALOHArandom access signalling requests from the remote ship terminals. Theproposed frame format for this signalling packet is shown in FIG. 1.This particular frame format and the Inmarsat-C channel parameters havebeen used as a representative mobile environment to design anddemonstrate the efficacy of the preambleless frequency acquisitionalgorithms that were developed.

The selected representative preambleless data packet has the followingcharacteristics, as obtained from the Inmarsat-C System DefinitionManual, for the second generation format shown in FIG. 1 (having a rateof 1200 symbols/sec): No acquisition preamble of any sort; the TDMA datapacket starts with a 64 bit unique word; and the data segment is 252rate-1/2 convolutionally encoded bits, to yield a packet size of 316bits (632 for the 600 symbol/sec case). The timeslot width is 370 symbolperiods (740 for the 600 symbol/sec case). The severe channel operatingconstraints include BPSK modulation at the low rate of 600 and 1200symbols/sec; a carrier frequency uncertainty of ±1450 Hz; a short termDoppler rate of 65 Hz/sec with a maximum range of ±50 Hz; an operatingE_(s) /N_(o) of 4.7 dB at the demodulator input; slot timing uncertaintyof ±27 symbols; and finally, a carrier-to-multipath ratio of 7 dB with aRician fading bandwidth of 0.7 Hz. As will be seen below, testing of theinvention was carried out in accordance with these parameters.

These constraints impose very challenging processing requirements forthe preambleless demodulator in order to successfully receive and detecteach preambleless packet under the worst possible channel environmentand slot timing uncertainties. As now will be described, sophisticatedacquisition algorithms that function in this hostile channel environmenthave been developed and implemented successfully in DSP-based hardware.Test data obtained with the hardware implementation and a specializedtest fixture indicate excellent correspondence with the expectedacquisition performance, as predicted by high-level computer simulationas well as theory. These results will be summarized below.

In the following, it is assumed that an MPSK modulated signal hasundergone IF conversion to baseband, and that both the in-phase andquadrature (I and Q) components are available to thedigitally-implemented demodulator. The baseband received signal willcontain a main spectral lobe within the frequency range ±R_(s), whereR_(s) is the symbol rate. Given a large frequency uncertainty, ±f_(c),in the received carrier due to Doppler shifts anddownconverter/upconverter translation errors, the total receiverone-sided bandwidth must be greater than (R_(s) +f_(c)). This representsa lower bound on the receiver input filter bandwidth. In general,however, the channel spacing determines the filter bandwidth. Thereceiver I and Q channel filters must exhibit a very sharp rolloff inorder to minimize adjacent channel interference. The frequencyacquisition technique described herein assumes the presence of suchchannel filters to limit the out-of-band noise and adjacent channelinterference. Since the I and Q analog-to-digital (A/D) convertermodules preceding the digital demodulator require anti-aliasing filters,this is not a problem. The channel filters also serve as anti-aliasingfilters.

The first step in the frequency acquisition method consists of computinga series of time-hopped windowed DFT/FFTs (called "periodograms"), andaveraging the energy magnitudes over the duration of a burst to reducenoise and fading effects. Given a sequence of samples, x(n), it ispossible to form K sub-sequences x_(r) (n), r=1,2, . . . , K, of lengthL spaced L/2 samples apart. For each sub-sequence, the windowed DFT/FFTX_(r) (m) is given by the following equation: ##EQU1## where w(n) is thewindow function.

The periodogram I_(r) (f_(m)) is equal to the squared magnitude of anDFT/FFT bin:

    I.sub.r (f.sub.m)=|Xr(m)|.sup.2

where ##EQU2## The unnormalized power spectral density is then: ##EQU3##

The effect of the modulation is first removed by squaring the complexinputs (for BPSK modulation). This concentrates most of the signalenergy at a single frequency equal to twice the modulated carrierfrequency. Although the squaring of the signal results in a loss in theoperating signal-to-noise ratio, this loss is regained due to theaveraging process performed on the signal strength estimates. Only the256 symbols (2048 samples) in the middle of a timeslot assumed tocontain the carrier are processed. The remaining symbols at thebeginning and end of the timeslot are discarded due to burst locationuncertainty. At a sampling frequency of f_(s) =9600 samples/sec, a 64point DFT/FFT provides a resolution of 150 Hz. The resolution isincreased to 75 Hz since the estimate of the squared data must bedivided by two.

The 2048 data samples are divided into 64 blocks of 64 samples each(K=L=64), with each block overlapping adjacent blocks by 32 samples.Each block is multiplied by a 64 point Blackman window. A Blackmanwindow has a very broad transition width so that a carrier located atthe very edge of an DFT/FFT frequency bin will be attenuated only 1.1dB, as compared to 3.9 dB for a rectangular window. The carrierfrequency is determined by choosing the bin containing the maximum powerspectrum. Because the range of the frequency search is limited to ±1450Hz, the DFT/FFT algorithm can be reduced to only 40 DFT/FFT outputs. Theentire calculation is very efficient when written with in-line code in aDSP chip because the small DFT/FFT size allows exclusive use of thechip's internal data RAM. The total number of processor instructioncycles is approximately 175,000.

The frequency estimator will locate a peak regardless of the presence ofa carrier. Burst presence can be detected by computing the peak/averageenergy ratio. The peak energy is simply the energy of the periodogramcontaining the maximum energy. The average energy is the average of theother 39 periodograms. If the ratio is greater than a predeterminedthreshold, then a burst has been detected. This method is very reliableover a wide dynamic range, eliminating the need for gain control.Simulations indicate that a threshold near 2.0 produces good resultsdown to E_(s) /N_(o) =2 dB.

The accuracy of the estimate is increased to within several Hz(depending on the amount of Doppler shift across a burst) using the finefrequency estimator. The 40 complex outputs of all 64 DFT/FFTs arestored in memory. The 64 values corresponding to the DFT/FFT bincontaining the carrier can be viewed as a decimated time series of theoriginal input, with a decimation factor of 64. If the carrier islocated in bin M, the time series X_(r) (M) is a bandpass filteredversion of x_(r) (n) filtered around the carrier frequency by thewindowed Fourier coefficients. Thus, if the series is processed byanother L-point DFT/FFT and the bin with the maximum squared magnitudeis selected, the resolution of the estimate can be increased by a factorof L. For the representative case of L=64, the fine frequency estimatorresolution is 1.2 Hz, assuming no carrier frequency drift over themeasurement interval. For mobile satellite applications, the actualresolution is limited by short-term Doppler effects and is on the orderof 5-10 Hz.

Demodulation of the stored complex samples by the estimated frequencycan be performed by multiplying the samples by [cos(2πfnT)+jsin(2πfnT)].The sine and cosine values are obtained from a look-up table.Precautions need to be taken in minimizing the truncation error whilecalculating the argument 2πfnT.

Looking now at a hardware implementation of the invention, as seen inFIG. 2, the DSP-based demodulator accepts a complex sampled basebandinput either from a pair of A/D converters connected to the IFdownconverter unit, or from a personal computer capable of generatingsimulated real-time channel packet data for test purposes.

An input buffer 205 stores complex input samples for an entire burstduration before processing begins, thus allowing the burst to bereprocessed during several passes to recover the final data. The bufferis controlled by an external slot timing pulse which marks the beginningof a burst timeslot. The actual burst location can be anywhere withinthe first 54 symbols allowed for guard time. The Inmarsat-C slottedALOHA protocol presents several difficult problems for burstacquisition, as was outlined above. The usage of each burst timeslot inthe signaling channel is random, and a given timeslot may be empty ormay contain a collision from two or more remote transmitters.

The first step in burst acquisition is estimation of the carrierfrequency offset. The frequency acquisition algorithm is the mostcritical to successful demodulator performance since it must also detectsignal presence at a very low signal to noise (S/N) ratio (1.5 dB for anE_(s) /N_(o) of 4.7 dB) because of the large extra input bandwidthrequired to allow for frequency uncertainty. A simple energy detector isineffective for burst presence detection since the signal and noiseenergies are nearly equal. Frequency acquisition is performed in twosteps. Coarse acquisition in coarse frequency estimator 220 estimatesthe carrier frequency to within 75 Hz, and fine acquisition in finefrequency estimator 230 narrows the uncertainty down to 10 Hz. The datain the input buffer 205 is corrected for frequency offset using acomplex multiplication by the sine and cosine of the carrier frequencygenerated from look-up tables.

Symbol timing adjustments are performed digitally in software. Aconventional A/D sample clock adjustment circuit cannot be used, as anentire burst is sampled before symbol timing is acquired. Thefrequency-corrected samples are first match filtered. Symbol timing thenis acquired, and the match filter output delay line is shifted to theproper timing phase and decimated to the symbol rate of 1200symbols/sec.

After symbol timing comes the removal of the burst time uncertainty,correction for the Doppler shift, and detection of the phase-coherentdata. The burst location is acquired with a non-coherent unique word(UW) correlator 250. Coherent correlation is not possible because at themaximum Doppler rate of 65 Hz/sec, the carrier phase will driftsignificantly over the duration of the UW. The UW correlator 250 servesa second function in addition to slot timing acquisition. If themagnitude of the correlation exceeds a predetermined threshold, then avalid packet has been received. Otherwise a packet collision is declaredand the data is ignored.

Coherent data detection is not possible unless the Doppler shift isremoved. The Doppler estimator/smoother 260 calculates a frequencyoffset for each symbol and correction is accomplished with a complexmultiplication stage. The Doppler-corrected symbols will have arbitrarycarrier phase, and the phase estimator 270 measures the phase offset andadjusts each symbol to the zero degree phase reference. The estimator270 is able to detect approaching cycle slips and compensate for thembefore they occur. A coherent UW correlation is performed on the outputof the phase detector to correct for the inherent 180 degree phaseambiguity of BPSK modulation. The final data, along with statusinformation, is sent to the host processor, where Viterbi decoding, dataformatting, and cyclic redundancy check (CRC) are performed. Furtherdetails of the major demodulator algorithms are provided below.

With respect to frequency acquisition, the requirement of detectingsignal presence/packet collisions as well as accurately measuring thecarrier frequency of a BPSK-modulated signal at an input S/N near 0 dBis especially severe. The inventive DFT/FFT-based spectral estimationtechnique was found to be very robust and readily suited for DSPimplementation. As mentioned above, the method consists of computing aseries of time-hopped windowed DFT/FFTs and averaging the energymagnitudes over the duration of a burst to reduce noise and fadingeffects. The DFT/FFT bin with the maximum average energy is presumed tocontain the carrier. A burst detection algorithm, to be described below,detects the presence of the burst from the energies in the DFT/FFT bins.Further processing using a similar DFT/FFT technique increases thefrequency resolution to well within the Doppler tracker range. Themethod is very reliable over a wide dynamic range. An optimal thresholdhas been obtained through simulation, as will be described, yieldingexcellent results.

As for matched filtering, the lack of any kind of pulse shaping at thetransmit side results in a simple integrate and dump matched filterstructure at the receive side. Since the symbol timing has not yet beendetermined, demodulated samples are processed through this filter withthe outputs computed at the sample rate. Once the symbol timing has beenestablished, the filter output is decimated to the symbol rate.

Symbol synchronization is achieved by first calculating a timing errorvector W between the signal envelope and two suitable selectedquadrature symbol timing references, P(n) and Q(n). The error vector,W=U+jV, is then used to estimate the timing phase difference bycalculating arctan (V/U). The real and imaginary components of thetiming error vector, U and V, are obtained from correlating the envelopeof the matched filter output with the two timing references. After thesymbol timing has been calculated, it is rounded to the nearest timingphase step, and the proper output of the matched filter is selected.

The symbol rate stability of the transmitter is given as ±1 part per10⁵. Therefore, under worst case conditions, the symbol rate couldchange by 10⁻³ degrees during one signaling packet interval. This isnegligible; hence, a single symbol timing estimate is sufficient foreach packet.

UW correlation is performed after symbol timing has been established,but before removal of Doppler frequency offset and carrier phaserecovery. The 64 data symbols to be correlated with the UW pattern aredivided down into several subgroups. The correlation results of thesesubgroups with the proper part of the UW sequence are then added andused to determine the location of the UW sequence in the packet.

The Doppler tracker (FIG. 3) must reduce the carrier frequency error toless than 2 Hz to prevent a complete phase reversal in 316 symbols. Thetracker removes any residual frequency error from the frequencyacquisition stage as well as removing the Doppler. The tracker isessentially open-loop, to prevent error propagation caused by impulsenoise. Because the Doppler rate is well behaved, only a small number ofestimates are computed using contiguous N-symbol blocks. N issufficiently large to reduce the variance of the estimate to much lessthan 1 Hz. Although the Doppler may drift significantly between twoestimates, it is assumed that the Doppler shifts undergo sinusoidalchanges. Therefore, the Doppler frequency associated with each symbolcan be computed by an appropriate smoothing function between twoestimates.

Two separate estimators are employed for increased accuracy. The complexsymbols output from the input processing block are applied to bothestimators. The first, coarse estimator 220 employs a discrete Fouriertransform (DFT)-based technique to estimate the Doppler frequency. Asecond, fine estimator 230 is employed to substantially increaseresolution. The estimates are sent to the post-processor block, and anew Doppler phase angle is calculated for each symbol. The phase updatesdrive a numerically controlled oscillator which is used for the Dopplercorrection of the matched filtered symbols.

The Doppler post-processor ensures that the Doppler corrections do notsuffer from appreciable phase jitter. The phase tracker (FIG. 4) adjuststhe Doppler-corrected symbols to the zero-degree phase reference inorder to perform bit detection. A very simple algorithm is employed thatis essentially open-loop, again providing very fast recovery from noisebursts. The complex symbols are squared to remove modulation effects,and then the real and imaginary components are averaged over a block of±M symbols to give an average two-dimensional carrier phase coordinate.The carrier phase can be derived by making an arctangent calculationusing a power series approximation. The input symbols are then rotatedby an NCO so that one of the two BPSK modulated symbols falls at zerodegrees. A 0/1 bit decision is made based on the sign of the realcomponent of the rotated symbols.

The carrier phase normally rotates quite slowly, but occasionalcorrections must be fed back to the Doppler tracker to maintain a phaseless than 180 degrees, or else cycle slips would occur. Thesecorrections ensure that the first symbol of the next block will have aphase offset near zero degrees. The final bit decision is passed to thehost processor for subsequent Viterbi decoding.

FIG. 5 is a high-level block diagram of the DSP-based demodulatorhardware. The demodulator operates on baseband received digitized inputsobtained from the output of the IF down-converter or a personal computertest interface. High speed erasable programmable read-only memory(EPROM) program memory 510 and random access memory (RAM) data memory520 are used so that the external memory is addressed without waitstates. Extensive use of programmable logic devices yields a compactdesign for the DSP peripheral logic, such as the address decoders,memory control signals, port decoders, and I/O interfacing. Suchimplementation is well known to those of working skill in thistechnological field, so further detailed description of this aspect ofthe invention is not believed necessary.

Communication between the demodulator 500 and the host processor 550takes place through a high-speed global RAM 525 connected to eachprocessor bus. Output ports for data and other status monitoring andcontrol signals are provided.

To test the inventive demodulator, a special personal computer-basedtest setup has been designed using the simulated test data with channelimpairments. As shown in FIG. 6, the test files, generated on a larger,minicomputer or mainframe computer (a VAX-11/750 is identified in FIG.6), were downloaded to a personal computer. User selectable frequencyoffsets, Doppler shifts, noise levels, delays, and symbol timing offsetswithin the slot could be entered on the larger computer during filecreation. Test program modules were written on the personal computer toformat the data file and download the sampled values to the demodulatorboard via a parallel port interface. Demodulated data then was uploadedfrom the DSP emulator to the personal computer through a serial port,where another program compared it with the transmitted packet andreported the error statistics.

The preambleless signaling demodulator was tested at a symbol rate of1200 bit/sec for frequency offsets ranging between ±1450 Hz, sinusoidalDoppler shifts of 65 Hz/sec with a range of ±50 Hz, E_(s) /N_(o) valuesfrom 2 to 6 dB and the reference noiseless case, symbol timing offsetsbetween ±180 degrees in 45 degree steps, and slot timing uncertainty inthe range of ±27 symbols. With no noise, the inventive demodulatorrecovered the data successfully, with no errors, under all of the aboveconditions. At the specified operating E_(s) /N_(o) of 4.7 dB, anaverage of 2.7 raw errors per packet (316 symbols) were detected. Thisresult compares well with the limiting theoretical value of 2.4 errorsper packet, representing performance within 0.2 dB of the theoreticalbit error rate (BER) curve. The error statistics indicate that no packeterrors will be experienced after Viterbi decoding (to be performed bythe host processor). Representative test results are provided in Table1.

                                      TABLE 1                                     __________________________________________________________________________    Representative Measured Test Results for the Preambleless Demodulator         Input Parameters          Measured Values  Errors per                         E.sub.S /N.sub.O                                                                       Doppler    Slot Delay       Slot Delay                                                                          packet (in                         dB   f.sub.S (Hz)                                                                      on/off                                                                             ΔT (deg.)                                                                     sym   f.sub.S (Hz)                                                                       ΔT (deg.)                                                                     sym   symbols)                           __________________________________________________________________________    No Noise                                                                           0   off  0     4     0    0     4     None                               No Noise                                                                           +1450                                                                             off  +180  3     +1450.75                                                                           +180  3     None                               No Noise                                                                           -1450                                                                             off  +180  3     -1450.81                                                                           +180  3     None                               No Noise                                                                           +1450                                                                             on   +180  3     +1460.13                                                                           +180  3     None                               No Noise                                                                           -1450                                                                             on   +180  3     -1439.06                                                                           +180  3     None                               4.7  0   on   +180  3     +9.38                                                                              +180  3     4                                  4.7  +1450                                                                             on   +45   3     +1460.13                                                                           +45   3     2                                  4.7  -1450                                                                             on   -45   3     +1441.44                                                                           -45   3     1                                  4.7  +953                                                                              on   -180  4     +963.25                                                                            +180  4     3                                  4.7  +1450                                                                             on   0     53    +1460.13                                                                           0     53    4                                  3.0  -1450                                                                             on   -180  3     -1439.06                                                                           -180  3     9                                  2.0  +725                                                                              on   0     53    +733.56                                                                            0     53    12                                 __________________________________________________________________________

As has been described, in accordance with the present invention, acompact, low cost, low complexity DSP-based preambleless demodulatoremploys powerful digital signal processing techniques to detect andacquire the carrier frequency offset and symbol timing under high noiseconditions, as well as to track Doppler and short term variations insignal amplitude because of multipath fading. As a result, it ispossible to acquire and demodulate the short burst packets without anyacquisition preamble. It is noted that, while the invention has beendescribed with reference to mobile and maritime satellite andterrestrial communication networks that use very short burst packets foraccess request and response channels (an application for the maritimeInmarsat-C system having been described in detail), it can be seen thatthe invention also has wider ranging applications.

With future enhancements to DSP technology and repackaging for mediumand high-volume production, the entire preambleless demodulator can beproduced easily in a very compact package at even higher symbol rates.Software changes also can be introduced to extend the operating bitrate, change the modulation format, or customize the operatingparameters for the Doppler multipath fading according to the desiredchannel conditions. This technology also lends itself to other low bitrate systems, where the existing preambles may now be shortened ordiscarded altogether, if the digital implementation approach describedherein is adopted.

The frequency acquisition algorithm just described for the Inmarsat-CCES signalling and message channel demodulators was optimized foroperation at 1200 bit/sec, representing the second generation ofservice. With the first generation service introduction at 600 bit/sec,the inventors investigated whether the inventive technique would stillfunction reliably at the lower rate. It was found that in the 600bit/sec mode the current algorithm would still work reliably at an E_(s)/N_(o) of 4.7 dB, but with a margin of less than 1 dB. Therefore, inorder to operate reliably at 600 bit/sec in presence of multipathfading, an enhancement to the current frequency estimation algorithm wasconsidered to be desirable.

In view of the foregoing, in accordance with another embodiment of thepresent invention, another enhanced frequency acquisition algorithm thataddresses this issue is discussed herein. The reliable operation of thenew algorithm for the first generation, at an E_(s) /N_(o) of 0 dB hasbeen validated. This technique can also be applied to the secondgeneration service at 1200 bit/sec for improved acquisition performance.

The Inmarsat-C CES signalling and message demodulators operate onbaseband complex samples. With BPSK modulation and no pulse shapingpresent on the link, the one-sided bandwidth of the input signalspectrum is equal to R_(s), the symbol rate. However, due to the largecarrier frequency offset present in the Inmarsat-C signalling andmessage channels (±1500 Hz), a relatively wide bandwidth anti-aliasingfilter is required at the inputs to the demodulators. For the 1200bit/sec mode of operation (C/N_(o) =35.5 dB-Hz), the required one-sidedfilter bandwidth is 2700 Hz, while for the 600 bit/sec mode (C/N_(o)=32.5 dB-Hz) this bandwidth can only be reduced to 2100 Hz. Thecarrier-to-noise power is given by: ##EQU4## where B is the one-sidedfilter bandwidth. With the operating E_(s) /N_(o) =4.7 dB for both modesand the filter bandwidths as above, the carrier-to-noise power ratios atthe demodulator input are 1.2 dB for R_(s) =1200 bit/sec, and -0.7 dBfor R_(s) =600 bit/sec. Therefore, a loss of approximately 2 dB in theacquisition performance of the 600 bit/sec mode compared to the 1200bit/sec mode is expected.

The frequency acquisition algorithm in accordance with the firstembodiment of the invention, as has been described, consists of twoDiscrete Fourier Transform (DFT) stages. The first stage (i.e., thecoarse frequency estimator) consists of 64-point hopping Fast FourierTransforms (FFT) which operate on the squared input samples. As thecarrier to noise ratio (C/N) is reduced below 0 dB, the squaring lossincreases exponentially. This loss, combined with the 2 dB drop in theinput C/N due to the wider filter bandwidth, would limit the performanceof the frequency acquisition algorithm in the 600 bit/sec mode.Accordingly, in accordance with the second embodiment of the invention,another frequency acquisition algorithm has been devised in order toimprove the demodulator performance at 600 bit/sec. This embodiment nowwill be described.

The second embodiment also uses the DFT/FFT concept, as in the firstembodiment. In order to reduce the noise bandwidth of the input to thecoarse frequency estimator, an extra coarse frequency estimator,providing carrier frequency estimates to within ±150 Hz, is utilized.Operation of the extra coarse frequency stage does not require squaringof the samples. This permits reliable operation for this stage atnegative values of C/N. After the extra coarse estimation stage, thereceived signal spectrum is processed by a narrowband filter ofbandwidth 1200 Hz, centered at the estimated carrier frequency. Afterthe filtered data is demodulated by a locally generated carrier at theestimated frequency, it is input to the currently implemented frequencyacquisition stages. The filtering operation increases the C/N at theinput to the second stage and hence the loss associated with thesquaring operation of the second stage is less severe. The introductionof the extra coarse stage (which would precede the coarse stage 220 inFIG. 2) reduces the search range of the next stage. Hence, thecomputational requirements should not be worse than in the firstembodiment. Further details on the algorithm now will be provided.

Block diagrams of the frequency acquisition schemes in accordance withthe first and second embodiments are shown in FIGS. 7 and 8,respectively. The extra coarse frequency stage of the new algorithmconsists of a series of 8-point DFTs sliding in time. At 600 bit/sec anda sampling rate of 4800 Hz, the frequency bin width is 1200 Hz. A 300 Hzfrequency step size (i.e., resolution) was chosen. Since the frequencyrange of interest is ±1500 Hz, 11 outputs need to be calculated.

The spectrum of the N-point sequence, x(n), at point ##EQU5## on theunit circle is given by:

    S.sub.z.sbsb.1 (n)=x(n)+x(n-1)z.sub.1.sup.-1 +. . . +x(n-N+1)z.sub.1.sup.-(N-1)

which is equivalent to a finite impulse response (FIR) filteringoperation. If the extra coarse frequency estimate is exact, this is alsoequivalent to a matched filtering operation for unfiltered BPSKtransmission. The filter impulse response is given by h(n)=z₁ ^(-n),0≦n≦N-1.

With z₁ ^(-n) =e^(j2)πk/N, the frequency response of this filter isgiven by: ##EQU6## which has the form ##EQU7## The width of the mainlobe of the response is ##EQU8## Therefore, the DFT can be representedby k FIR filters, each having the above response centered at kf_(s) /N.

The inputs to the demodulator (f_(s) =4800 Hz) are windowed by a Hammingwindow and then are processed by the above DFTs, with each DFT hopped bytwo samples. Hence, the outputs of the DFTs are equivalent to the inputsignal filtered by bandpass filters of total width 1200 Hz, centered atthe DFT frequencies (i.e., 0 Hz, ±600 Hz, etc.) and then decimated 2:1.The hopping and decimation steps are desired so as to reduce thesampling rate and hence the computational requirements of the subsequentstages. A minimum output sampling rate of 2400 Hz is required to avoidaliasing.

If the signal is centered exactly at one of the DFT frequencies, theshape of the filter is matched to the signal spectrum. In generalhowever, a small mismatch will occur which is of no concern since onlythe peak of the spectrum needs to be located, and since no furtherprocessing on this spectrum will be done. Also, introduction of aHamming window results in improved performance over a rectangularwindow. The Hamming window has a wider transition region and highersidelobe attenuation than the rectangular window. Hence, in case of amismatch, more of the signal spectrum is preserved with a Hamming windowthan with a rectangular window.

The DFT output for the frequency bin corresponding to the maximummagnitude is selected as the likely signal, and then demodulated by alocally generated carrier with a frequency value corresponding to theselected bin. Hence, the frequency uncertainty is now reduced to ±150Hz. The subsequent processing stages are similar to the ones currentlyused. The demodulated signal is then squared, windowed by a Blackmanwindow, and processed through a series of 64-point DFTs. Because of thesquaring operation, the frequency uncertainty is increased to ±300 Hz.The sampling rate at this stage is 2400 Hz, yielding a resolution of37.5 Hz with a 64-point DFT. Twenty-three DFT outputs are calculated tocover the ±300 Hz uncertainty range, with additional margin. Asmentioned before, if the carrier frequency does not coincide with one ofthe DFT frequencies of the extra coarse stage, the signal spectrum willbe somewhat distorted by the DFT's "filtering" operation; however, thecarrier frequency information is still present.

The DFT output of the second stage with the maximum magnitude isfrequency corrected by the coarse frequency estimate, and input to thefine frequency acquisition stage which consists of a single 16-pointDFT. For this stage the frequency uncertainty is ±37.5 Hz, and thesampling rate is reduced to 75 Hz. The frequency resolution for this DFTis about 4.69 Hz. Therefore, 17 outputs are calculated. After divisionby two, to account for the squaring operation, the resolution isimproved to 2.3 Hz.

The operation of the first two stages of the algorithm were simulated atE_(s) /N_(o) values of 0 and 1 dB. The results, shown below in Table 2,were obtained by processing 500 signalling channel packets withuniformly distributed frequency offsets in the range ±1500 Hz. Theresults show that error free frequency estimates are obtained at E_(s)/N_(o) =1 dB.

                  TABLE 2                                                         ______________________________________                                        Simulation Results for the New Frequency Acquisition                          Algorithm, Using the DFT's "Filtering" Operation                              E.sub.s /N.sub.o                                                                        Noise Seed 100128                                                                             Noise Seed 91682                                    ______________________________________                                        1 dB      Missed 0/500     Missed 0/500                                       0 dB      Missed 10/500    Missed 5/500                                       ______________________________________                                    

Since the misses at an E_(s) /N_(o) of 0 dB were mostly caused by thesecond (i.e., the coarse) frequency acquisition stage, it seemedworthwhile to determine if this was in turn caused by the distortion ofthe received spectrum introduced by the first (i.e. the extra coarse)stage. Hence, the simulation program was changed such that the"filtering" operation of the first stage was replaced by an InfiniteImpulse Response (IIR) filter, yielding a modification of the secondembodiment of the invention. The demodulation operation then wasperformed on the delayed input samples instead of the DFT outputs. Ablock diagram of this modified second embodiment is shown in FIG. 9. Theresults obtained at E_(s) /N_(o) =0 dB for each filter bandwidth areshown in Table 3.

                  TABLE 3                                                         ______________________________________                                        Simulation Results at E.sub.s N.sub.o of 0 dB for the New                     Frequency Acquisition Algorithm, Using the IIR Filters                        IIR Filter Bandwidth                                                                       Noise Seed 100128                                                                           Noise Seed 91682                                   ______________________________________                                        0.75 kHz     Missed 29/500 Missed 18/500                                       0.5 kHz     Missed 8/500  Missed 3/500                                        0.3 kHz     Missed 39/500 Missed 40/500                                      ______________________________________                                    

Table 3 shows that the acquisition performance degrades if the filterbandwidth is too wide (enough noise power is not rejected), or toonarrow (the signal spectrum is not preserved adequately).

Thus, according to the modified second embodiment of the invention, withthe IIR filter bandwidth of 0.5 kHz, the acquisition performance at anE_(s) /N_(o) of 0 dB is slightly better than the second embodiment shownin FIG. 8. The trade-off between the two methods also involves thefaster execution and larger storage space of the second embodiment,shown in FIG. 8, versus the slower execution and smaller storage spaceneeded for the IIR filter method, shown in FIG. 9 (no DFT outputs needto be stored). Considering the close performance of the two techniquesat an E_(s) /N_(o) of 0 dB, which is significantly below the nominaloperating E_(s) /N_(o) of 4.7 dB, it would appear to be more desirableto employ the technique exemplified in FIG. 8, which employs no externalIIR filters.

The technique of FIG. 8 also may be implemented desirably for the 1200bit/sec mode in order to improve the acquisition performance, andminimize the software differences between the two operating modes. Withthe current signalling channel IF test results indicating reliableoperation at an E_(s) /N_(o) of 2 dB, introduction of this new schemecould improve the acquisition performance of the 1200 bit/sec mode tolower E_(s) /N_(o) values.

The overall structure for the three-stage frequency estimator inaccordance with the second embodiment of the invention is illustrated inFIG. 10. The complex analog input is filtered by antialiasing filter1001 and sampled by A/D converter 1002 at a sample rate of F_(S). Theestimator requires a block of N complex samples of a burst transmissionstored in its input buffer 1003. Stage 1 provides a rough estimate, F,of f_(c) directly from the MPSK-modulated signal by computing a seriesof DFT calculations at block 1103, the DFT calculations being hopped intime. The time-hopped complex DFT outputs are bandpass filtered versionsof the input signal with a two-sided bandwidth of approximately 2 R_(S).In addition, the time-hopping process decimates the sampling rate to alower value. Thus the DFT calculation simultaneously provides theinitial carrier frequency estimate, bandpass filters the input signal,and decimates the sampling rate to approximately 2 R_(S). The fact thatthese three operations are combined in this manner greatly reduces thetotal number of calculations required. The sample rate decimation alsoreduces the complexity of the following stages. For an initialuncertainty f_(c) >R_(s), the bandpass filtering operation improves thesignal-to-noise ratio by more than 3 dB. The filtered samples arerotated by -F₁ 1108, reducing the carrier frequency to f_(c) -F₁ beforebeing processed in stage 2.

The MPSK modulation is then removed by raising the stage 1 outputsamples to the M'th power at block 1200. Thus the signal consists of asingle carrier at a frequency of M(f_(c) -F₁). In a manner nearlyidentical to stage 1, stage 2 provides a higher resolution estimate, F₂,of the residual frequency error and simultaneously bandpass filters thecarrier signal to a much narrower bandwidth to permit simultaneousdecimation to a lower sample rate. The samples are rotated by -F₂ inblock 1208, reducing the carrier frequency to f_(c) -F₁ -F₂.

A high resolution frequency estimate, F₃, is obtained in stage 3 bydoing an FFT operation on the stage 2 output samples. Finally the threeestimates are summed at block 1401 to give the final, high-resolutionestimate: ##EQU9##

Details of the three frequency estimators are provided below. Theexample packet format of FIG. 1, described in detail above, was used forthe testing.

As described above, the frequency acquisition method used in the firsttwo stages consists of computing a series of time-hopped windowed DFTs(called "periodograms"), and averaging the energy magnitudes over theduration of a transmission burst to reduce noise and fading effects.Given a sequence of N buffered complex samples, x(n), where n=0, 1, 2, .. . , N-1, in block 1003, it is possible to form K subsequences x_(r)(n), r=1, 2, . . . , K, of length L spaced J samples apart.

For each of the K subsequences, the windowed DFT X_(r) (k) is given bythe following equation: ##EQU10## where W(n) is the window function

k=DFT frequency bin number.

The foregoing equation is computed in block 1103 for stage 1 usingKaiser window function 1102. The calculation is performed for all valuesof k within the desired frequency range and repeated for all K₁subsequences.

The periodogram I_(r) (f_(k)) is equal to the squared magnitude of a DFTbin:

    I.sub.r (f.sub.k)=|X.sub.r (k)|.sup.2    (3)

where ##EQU11## The unnormalized power spectral density is then:##EQU12## In stage 1 the periodogram I_(r) (f_(k)) is computed in block1104 for all K₁ subsequences and for all frequency bin numbers, k,within the frequency range of interest. S_(x) (f_(k)) is computed inblock 1105.

The power spectral density is simply a sum of the periodograms of eachsubsequence and the normalized carrier frequency is given by f_(k) forthe value of k which maximizes S_(x) (f_(k)). Thus the frequencyestimate is obtained by searching for the maximum S_(x) (f_(k)) for allvalues of k (block 1106 in stage 1). The step size and range of k isarbitrary and depends on the application. If the DFT is implemented as aFast Fourier Transform (FFT), then k takes on the values 0, 1, . . . ,L-1.

For the example case, N=2048 samples (256 symbols) and F_(s) =4800 Hz (8samples per symbol). Only the symbols in the middle of a TDMA timeslotassumed to contain the carrier are processed. The remaining symbols atthe beginning and end of the timeslot are discarded due to burstlocation uncertainty. For R_(s) =600 bit/s, the width of the mainspectral lobe is 600 Hz. For a sample rate of 4800 Hz, L₁ =8 provides aDFT bin width that matches the main spectral lobe of the BPSK-modulatedsignal (FIG. 11). A Kaiser window (block 1102) with parameter β=3.1 waschosen for the window function to maximize the average signal-to-noiseratio within a DFT bin for all expected values of frequency offsets. Thefrequency resolution of the first estimator is 300 Hz--i.e. k has a stepsize of 0.5. DFT outputs are computed for all values of k within therange of ±5.0 to span the total specified frequency uncertainty range of±1500 Hz. The first stage estimate, F₁, is k_(max) ·F_(s) /J₁, wherek_(max) corresponds to the DFT bin with the maximum power spectraldensity and J₁ represents the sample rate decimation ratio of stage 1.

Each complex DFT output X_(r) (k) can be thought of as an output at timer of a Finite Impulse Response (FIR) bandpass filter with impulseresponse W centered at frequency k. Thus the sequence X_(r) (k_(max)),r=1, 2, . . . , K₁ is a bandpass filtered version of the input signaland the signal-to-noise ratio is greatly improved. Since eachsubsequence is spaced J₁ input samples apart, the sequence X_(r)(k_(max)) has a sample rate decimated by a factor of J₁ compared to theinput sequence. X_(r) (k_(max)) is buffered in block 1107 for subsequentprocessing by stage 2.

J₁ must be chosen carefully to avoid aliasing effects. F_(s) /J₁ must begreater than the filtered signal bandwidth. The two-sided signalbandwidth of BPSK assuming no transmit filtering is approximately4R_(s). Therefore J₁ =2 and the decimated sample rate=2400 Hz. Thesequence X_(r) (k_(max)) stored in block 1107 is frequency corrected by-F₁ to greatly reduce the frequency offset (block 1108). Frequencycorrection of the stored complex samples can be performed by multiplyingthe samples by [cos(2πF₁ n/F_(s))-Jsin(2πF₁ n/F_(s))], where n is thesample index. The sine and cosine values are obtained from a look-uptable. Precautions need to be taken in minimizing the truncation errorwhile calculating the argument 2πF₁ n/F_(s).

Next, the modulation is removed in block 1200 by squaring the complexinputs (for BPSK modulation). This concentrates most of the signalenergy at a single frequency equal to twice the modulated carrierfrequency. Although the squaring of the signal results in a loss in theoperating signal-to-noise ratio, this loss is regained in the next stagedue to the averaging process performed on the DFT magnitudes.

The 1024 complex samples from stage 1 are divided into K₂ =31 blocks ofL₂ =64 symbols spaced J₂ =L₂ /2=32 symbols apart (block 1201). A spacingof L/2 produces the most reliable estimate versus the amount ofcomputations required. The periodograms are computed in a similar mannerto stage 1 using equations 2, 3, and 4 in blocks 1203, 1204, and 1205respectively. Each subsequence is multiplied by a 64 point Blackmanwindow in block 1202. A Blackman window has a very broad transitionwidth so that a carrier located at the very edge of a DFT frequency binwill be attenuated only 1.1 dB as compared to 3.9 dB for a rectangularwindow. At a sampling frequency of F_(s) =2400 samples/sec a 64 pointDFT provides a resolution of 37.5 Hz. The resolution is increased to18.75 Hz since the frequency estimate of the squared data is divided bytwo in block 1209. (In general, removing the modulation of M-ary PSK byraising the data samples to the Mth power increases the carrierfrequency by a factor of M.) Because the stage 1 frequency resolution is300 Hz, the stage 2 search can be limited to ±150 Hz. However, thesearch is extended to ±412.5 Hz (DFT frequency bins in the range k=±11)to compensate for estimation error in stage 1. A DFT can be implementedmore efficiently over the limited search range than the FFTimplementation. The frequency bin with the highest energy, k_(max), isassumed to contain the carrier and the estimate, F₂, is determined(block 1206). The stage 2 sequence X_(r) (k_(max)) can also be viewed asa bandpass filtered and decimated version of the stage 2 input data andis buffered in block 1207 for further processing. The output sample rateis decimated by a factor of L₂ /2 to 75 Hz. The 32 samples stored inblock 1207 are frequency corrected by -F₂ in block 1208 and then arefurther processed by stage 3.

The stage 2 output samples are truncated to one block of L₃ =16 complexsamples (block 1301) and a 16-point FFT calculation is performed inblock 1302. The FFT is more efficient than a DFT in this case. Thesquared magnitude of all 16 FFT outputs (k=0, 1, . . . , 15) iscalculated in block 1303. The frequency bin with the maximum magnitudeis selected in block 1304 and the frequency estimate F₃ is determinedwith a resolution of 4.69 Hz. The actual resolution is 2.34 Hz since theestimate is divided by two (block 1305) to compensate for the squaringoperation. For mobile satellite applications, the actual resolution islimited by short-term Doppler effects caused by motion of the mobileterminal and is on the order of 5 to 10 Hz.

The total frequency estimate then is the sum of the three individualestimates, as given in equation (1). Note that each stage attempts tocorrect for frequency errors in the previous stage by using an extendedfrequency search range.

The frequency estimator will always produce an output regardless of thepresence of a carrier. The carrier is assumed to reside in the DFTfrequency bin with the highest average energy. A good measure of thereliability of the estimate can be easily determined by the peak/averageenergy ratio, R, from stage 1 or 2. Normally a strong spectral peak isobserved in one frequency bin and low-level noise is observed in all theother bins. The peak energy is simply the average energy of theperiodogram containing the maximum energy (S_(x) (f_(kmax))). Theaverage energy is the average of all the periodograms for all othervalues of k. However, since significant carrier energy leakage can beobserved in frequency bins adjacent to k_(max), adjacent bins alsoshould be excluded from the average. Thus: ##EQU13##

This ratio is also a good means of detecting transmission burstactivity. If the ratio is greater than a predetermined threshold, then aburst has been detected. This method is very reliable over a widedynamic range, eliminating the need for gain control. Because a ratio iscomputed, a receiver gain factor would appear in both the numerator anddenominator and therefore be cancelled out. Simulations indicate that apeak/average energy ratio threshold near 2.0 produces good results downto E_(s) /N_(o) =2 dB.

While the invention has been described above in detail, various changesand modifications within the scope and spirit of the invention will beapparent to those of working skill in this technological field. Thus,the invention is to be considered as limited only by the scope of theappended claims.

What is claimed is:
 1. A digital preambleless demodulator comprising:aninput buffer for receiving an input signal which includes a carrier waveand providing a baseband output; a coarse frequency estimator, connectedto said input buffer, for providing a first estimation of a frequency ofsaid carrier wave, said first estimation being within a first frequencyband, said coarse frequency estimator comprising a first Fouriertransform module for performing either a first fast Fourier transform(FFT) or a first discrete Fourier transform (DFT) to provide said firstestimation; and a fine frequency estimator, receiving said firstestimation and providing a second estimation of said frequency of saidcarrier wave, said second estimation being within a second frequencyband that is narrower than said first frequency band, said finefrequency estimator comprising a second Fourier transform module forperforming either a second FFT or a second DFT on said first estimationto provide said second estimation; the foregoing arrangement being suchthat said frequency of said carrier wave can be acquired within apredetermined resolution without necessitating a preamble in said inputsignal.
 2. A digital preambleless demodulator as claimed in claim 1,wherein said first frequency band is ±75 Hz.
 3. A digital preamblelessdemodulator as claimed in claim 1, wherein said second frequency band is±10 Hz.
 4. A digital preambleless demodulator as claimed in claim 1,further comprising an extra coarse frequency estimator, disposed betweensaid coarse frequency estimator and said input buffer, for receivingsaid baseband output and providing a third estimation of said frequencyof said carrier wave, said third estimation being within a thirdfrequency band that is wider than said first frequency band, said extracoarse frequency estimator comprising a third Fourier transform modulefor performing either a third FFT or a third DFT on said baseband outputto provide said third estimation, said coarse frequency estimatorreceiving said third estimation and providing said first estimationaccordingly.
 5. A digital preambleless demodulator as claimed in claim4, wherein said third frequency band is ±150 Hz.
 6. A digitalpreambleless demodulator as claimed in claim 5, wherein said firstfrequency band is ±37.5 Hz.
 7. A digital preambleless demodulator asclaimed in claim 5, wherein said second frequency band is ±2.3 Hz.
 8. Adigital preambleless demodulator comprising:an input buffer forreceiving an input signal which includes a carrier wave and providing abaseband output; an extra coarse frequency estimator for receiving saidbaseband output and providing a first estimation of a frequency of saidcarrier wave, said first estimation being within a first frequency band,said extra coarse frequency estimator comprising a first Fouriertransform module for receiving said baseband output and performing afirst fast Fourier transform (FFT) or a first discrete Fourier transform(DFT) on said baseband output to provide said first estimation; a coarsefrequency estimator, connected to said extra coarse frequency estimator,for providing a second estimation of a frequency of said carrier wave,said second estimation being within a second frequency band that isnarrower than said first frequency band, said coarse frequency estimatorcomprising a second Fourier transform module for performing either asecond FFT or a second DFT on said first estimation to provide saidsecond estimation; and a fine frequency estimator, receiving said secondestimation and providing a third estimation of said frequency of saidcarrier wave, said third estimation being within a third frequency bandthat is narrower than said second frequency band, said fine frequencyestimator comprising a third Fourier transform module for performingeither a third FFT or a third DFT on said second estimation to providesaid third estimation; the foregoing arrangement being such that saidfrequency of said carrier wave can be acquired within a predeterminedresolution without necessitating a preamble in said input signal.
 9. Adigital preambleless demodulator as claimed in claim 8, wherein saidfirst frequency band is ±150 Hz.
 10. A digital preambleless demodulatoras claimed in claim 8, wherein said second frequency band is ±37.5 Hz.11. A digital preambleless demodulator as claimed in claim 8, whereinsaid third frequency band is ±2.3 Hz.
 12. A method of performing digitalpreambleless demodulation of an input signal, said methodcomprising:receiving an input signal which includes a carrier wave;performing a first fast Fourier transform (FFT) or a first discreteFourier transform (DFT) on said input signal to provide a firstestimation of said frequency of said carrier wave, said first estimationbeing within a first frequency band; and performing a second FFT or asecond DFT on said first estimation to provide a second estimation ofsaid frequency of said carrier wave, said second estimation being withina second frequency band that is narrower than said first frequency band.13. A method as claimed in claim 12, wherein said first frequency bandis ±75 Hz.
 14. A method as claimed in claim 12, wherein said secondfrequency band is ±10 Hz.
 15. A method as claimed in claim 12, furthercomprising the steps of performing a third FFT or a third DFT on saidinput signal to provide a third estimation of said frequency of saidcarrier wave, said third estimation being within a third frequency bandwhich is wider than said first frequency band, said first estimationbeing provided accordingly.
 16. A method as claimed in claim 15, whereinsaid first frequency band is ±150 Hz.
 17. A method as claimed in claim15, wherein said second frequency band is ±37.5 Hz.
 18. A method asclaimed in claim 15, wherein said third frequency band is ±2.3 Hz.